Sharp $L^p$ estimates for oscillatory integral operators of arbitrary signature

Abstract

The sharp range of $L^p$-estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase. This simultaneously generalises earlier work of the authors and Guth, which treats the maximal signature case, and also work of Stein and Bourgain--Guth, which treats the minimal signature case.

Introduction expanded. Figures added. 46 pages, 5 figures